IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005
485
Tuning a PID Controller for a Digital
Excitation Control System
Kiyong Kim,
Member, IEEE,
and Richard C. Schaefer
Abstract—Some
of the modern voltage regulator systems are
utilizing the proportional, integral, and derivative (PID) control
for stabilization. Two PID tuning approaches, pole placement and
pole–zero cancellation, are commonly utilized for commissioning
a digital excitation system. Each approach is discussed including
its performance with three excitation parameter variations. The
parameters considered include system loop gain, uncertain exciter
time constants, and forcing limits. This paper is intended for var-
ious engineers and technicians to provide a better understanding
of how the digital controller is tuned with pros and cons for each
method.
Index Terms—Excitation
system, loop gain, pole placement,
pole–zero cancellation, proportional, integral, and derivative
(PID) control, voltage overshoot, voltage response.
I. I
NTRODUCTION
T
ODAY’S digital excitation systems offer numerous bene-
fits for performance improvements and tuning over their
analog voltage regulator predecessors. The days of potentiome-
ters, screwdrivers, and voltmeters for tuning are replaced with
a laptop computer and a table and chair. Unlike the past, when
excitation systems were tuned by analog meters, today’s exci-
tation can be tuned very precisely to desired performance and
recorded into a file for future performance comparison in the
form of an oscillography record.
II. P
ROPORTIONAL
, I
NTEGRAL
,
AND
D
ERIVATIVE
(PID) C
ONTROL
Fig. 1. Simplified block diagrams of automatic voltage regulators.
The present-day digital regulator utilizes a PID controller in
the forward path to adjust the response of the system [1]. For
main field-excited systems, the derivative term is not utilized.
The proportional action produces a control action proportional
to the error signal. The proportional gain affects the rate of rise
after a change has been initiated into the control loop. The in-
tegral action produces an output that depends on the integral of
the error. The integral response of a continuous control system
is one that continuously changes in the direction to reduce the
error until the error is restored to zero. The derivative action
produces an output that depends on the rate of change of error.
For rotating exciters, the derivative gain is used which measures
Paper PID-04-19, presented at the 2004 IEEE Pulp and Paper Industry Con-
ference, Vancouver, BC, Canada, June 27–July 1, and approved for publication
in the IEEE T
RANSACTIONS ON
I
NDUSTRY
A
PPLICATIONS
by the Pulp and Paper
Industry Committee of the IEEE Industry Applications Society. Manuscript sub-
mitted for review July 1, 2004 and released for publication November 16, 2004.
The authors are with Basler Electric Company, Highland, IL 62040 USA
(e-mail: kiyongkim@basler.com; richschaefer@basler.com).
Digital Object Identifier 10.1109/TIA.2005.844368
the speed of the change in the measured parameter and causes
an exponentially decaying output in the direction to reduce the
error to zero. The derivative term is associated with the voltage
overshoot experienced after a voltage step change or a distur-
bance. The basic block diagram of a PID block utilized in the
automatic voltage regulator control loop is shown in Fig. 1. In
provides
addition to the PID block, the system loop gain
an adjustable term to compensate for variations in system input
voltage to the power converting bridge. When performance is
measured, the voltage rise time is noted at the 10% and 90%
levels of the voltage change. The faster the rise time, the faster
the voltage response [5].
The benefits of a fast excitation controller can improve the
transient stability of the generator connected to the system, or
stated another way, maximize the synchronizing torque to re-
store the rotor back to its steady state position after a fault. A
fast excitation system will also improve relay tripping coordi-
nation due to the excitation systems’ ability to restore terminal
voltage quickly, and providing more fault current to protective
relays for optimum tripping time.
III. C
HARACTERISTIC OF
E
XCITATION
C
ONTROL
S
YSTEMS
An optimally tuned excitation system offers benefits in
overall operating performance during transient conditions
caused by system faults, disturbances, or motor starting [5].
During motor starting, a fast excitation system will minimize
the generator voltage dip and reduce the
heating losses of
the motor. After a fault, a fast excitation system will improve
0093-9994/$20.00 © 2005 IEEE
486
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005
Fig. 4. One-line diagram.
Fig. 2.
Generator saturation curve illustrating generator gain.
the PID controller, the synchronous machine may become
oscillatory after a fault [8].
Besides the open-circuit voltage step test, another test per-
formed is the voltage step test with the generator breaker
closed. When voltage step tests are performed with the gen-
erator breaker closed, very small percentage voltage steps are
introduced to avoid large changes in generator vars. In this
case, a 1%–2% voltage step change is typical [7].
IV. T
UNING OF
PID C
ONTROLLER
The controller parameters are determined with several excita-
tion system parameters, such as voltage loop gain and open-cir-
cuit time constants [1]. These parameters vary with not only the
system loading condition but also gains dependent on the system
configuration, such as the input power voltage via power poten-
tial transformer (PPT) to the bridge rectifier as shown in Fig. 4.
Commissioning a new automatic voltage regulator (AVR) can
be a challenging task of checking excitation system data in a
short time, without any test data, and with no other link to the
actual equipment, except for an incomplete manufacturer’s data
sheet, or some typical data set.
To tune the digital controller, two methods are predominantly
used, one being the pole-placement method and the other being
the cancellation approach [1], [2]. To simplify the design of the
in Fig. 1.
PID controller, we assume
Every PID controller contains one pole and two zero terms
with low-pass filter in the derivative block ignored. For gen-
erators containing rotating exciters, the machine contains two
open-loop poles, one derived from the main field and the other
derived from the exciter field. A pole represents a phase lag in
the system while the zero tends to provide a phase lead compo-
nent. The location of poles and zeros with relation to the exciter
and generator field poles determines the performance of the ex-
citation control system.
Root locus is used to describe how the system responds based
upon gain in the system. Using the pole-placement method
and referencing Fig. 5(a), the poles of the generator main field
and exciter field are located on the real axis. The generator
main field pole is located close to the origin while the exciter
field pole is typically tens times the distance, the distance
depending upon the time constant of the exciter field versus
Fig. 3.
two.
Phase shift of the exciter field, the generator field, and the sum of the
the transient stability by holding up the system and providing
positive damping to system oscillations.
A fast excitation system offers numerous advantages, im-
proved relay coordination and first swing transient stability,
however an excitation system tuned too fast can potentially
cause megawatt instability if the machine is connected to a
voltage-weak transmission system. For these systems a power
system stabilizer may be required to supplement machine
damping.
The evaluation of system performance begins by performing
voltage step responses to examine the behavior of the excitation
system with the generator. It is performed with the generator
breaker open, since the open-circuited generator represents
the least stable condition, i.e., the highest gain and the least
saturation (see Fig. 2). Fig. 3 represents a Bode plot of the
generator and exciter field for a sweep frequency from 0 to
10 Hz. The frequency plot represents the potential voltage
oscillation frequency after a disturbance. The time constant
of the generator field and the exciter field is plotted and
illustrated to show that as the frequency increases, the phase
angle becomes more lagging. The phase angle of the generator
field adds directly with the phase angle of the exciter field. As
the phase angles add to 150 , the system will most likely become
unstable because of the combined gain of the generator and
the excitation system. Unless compensated properly through
KIM AND SCHAEFER: TUNING A PID CONTROLLER FOR A DIGITAL EXCITATION CONTROL SYSTEM
487
Fig. 6. 5% Voltage step response using pole-placement method.
the system response will be oscillatory. The conjugate pair
represents the ratio of the imaginary to real value of poles to
determine the voltage overshoot. The absolute value of the
pole determines the frequency of voltage oscillation. The faster
voltage response can be achieved by moving the poles from the
origin and the less oscillatory response with the smaller ratio
(see Fig. 5(b)).
A. Pole Placement
In the pole-placement method, the desired closed-loop pole
locations are decided on the basis of meeting a transient re-
sponse specification. The design forces the overall closed-loop
system to be a dominantly second-order system. Specifically,
we force the two dominant closed-loop poles (generator and
controller) to be a complex conjugate pair resulting in an un-
derdamped response. The third pole (exciter) is chosen to be a
real pole and is placed so that it does not affect the natural mode
of the voltage response. The effect of zeros on the transient re-
sponse is reduced by a certain amount of trial and error and en-
gineering judgment involved in the design.
The pole-placement method generally requires specific infor-
mation of the exciter field and main generator field time con-
stants to determine the gains needed for the digital controller
for adequate response. Voltage overshoot of at least 10%–15%
is anticipated with the pole-placement method with a 2–3-s total
voltage recovery time, although its voltage rise time can be less
than 1 s.
Fig. 6 illustrates the generator terminal voltage performance
of a 100-MW steam turbine generator when a 5% open-cir-
cuit voltage step change has been introduced. Generator voltage
overshoot is 20% with a total voltage recovery time of 2.5 s. The
, and
.
PID gains are as follows:
The excitation system bandwidth is used to characterize the
response of the generator with the voltage regulator. The wider
the voltage regulator bandwidth, the faster is the excitation
system.
To derive the voltage regulator bandwidth, the gain and phase
shift is plotted over a range of frequencies, typically, 0–10 Hz
Fig. 5. Root locus and voltage response with two different system
gains (
( )
). (a) Root locus of different loop gains gains:
=
= 70;
= 25
. (b) Step responses performance gains:
90;
= 90;
= 70;
= 25
.
K
K
K
K
K
K
K
the main field. The smaller the exciter field time constant,
the greater the distance. The PID controller consists of one
pole and two zeros.
Fig. 5(a) shows how the closed-loop poles move as the
represents the totalized
loop gain increases. The loop gain
gain that includes the generator, field forcing of the excitation
system, and PID controller. The open-loop zeros becomes the
closed-loop zeros and do not depend on the loop gain. On
the other hand, the poles of the closed-loop system (exciter,
generator, and controller) are moving toward zeros in a certain
path as the loop gain increases. The path of the closed-loop
poles depends on the relative location of poles and zeros based
upon its time constants. With fixed PID gains, a certain system
determines the closed-loop poles. Two cases of the
gain
closed poles are shown in Fig. 5(a), one for system gain 1.0 and
the other for system gain 0.13.
In general, the poles nearest to the origin determine the
system responses. When the poles become a conjugate pair,
488
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 2, MARCH/APRIL 2005
Fig. 9.
Fig. 7. Root locus for 100-MW generator using pole-placement method gains:
= 90;
= 70;
= 29;
= 15
.
Open-loop Bode diagram of pole-placement method.
K
K
K
K
Fig. 8.
Closed-loop Bode diagram of pole-placement method.
Fig. 10. Root locus for 100-MW generator using pole–zero cancellation
method gains:
= 80;
= 20;
= 40;
= 15
.
K
K
K
K
by applying a signal oscillator into the voltage regulator sum-
ming point. The input signal is compared to the generator output
signal by measuring the phase and gain of the frequency range
of 0–10 Hz, which represents the potential oscillating frequency
of the generator interconnected to the system. For these Bode
plots, information of the generator and exciter time constant
along with the excitation system gains are used to determine the
bandwidth of the generator excitation system.
A typical root locus with pole-placement method is shown in
Fig. 7. Notice how the closed-loop poles move along the circle
with increasing gain. Fig. 8 shows the phase lag, 59.1 at 3
dB. The decibel rise prior to roll-off confirms the voltage over-
shoot noted during the voltage step response in Fig. 6.
The ideal excitation system will maintain high gain with min-
imum phase lag. The point of interest is the degree of phase lag
and gain at 3 dB, the bandwidth of the excitation system. The
less phase lag with higher gain gives the better performance of
the excitation system. Fig. 9 highlights the open-loop response
of the excitation system. It shows the phase lag of 105 at 0
dB, crossover frequency.
B. Pole–Zero Cancellation
The cancellation method offers the benefit of performance
with minimum voltage overshoot. This method uses the fact
that the dynamic behavior of the pole is cancelled if the zero
is located close to the pole. The PID controller designed using
pole–zero cancellation method forces the two zeros resulting
from the PID controller to cancel the two poles of the system.
The placement of zeros is achieved via appropriate choice of
the PID controller gains. Since exciter and generator poles are
on the real axis, the controller has zeros lying on the real axis.
Unlike the pole-placement method that uses high integral gain,
a proportional gain is set to be at least four times greater than
the integral term.
A typical root locus with inexact cancellation is shown in
Fig. 10. The zeros are selected to cancel the poles corresponding
to exciter and generator time constants. Thus, the closed-loop
system will be dominantly first order.
The exciter and generator time constants vary with the
system condition. The exact pole–zero cancellation is not
KIM AND SCHAEFER: TUNING A PID CONTROLLER FOR A DIGITAL EXCITATION CONTROL SYSTEM
489
Fig. 12.
Closed-loop Bode diagram of pole–zero cancellation method.
Fig. 11.
Voltage response using pole–zero method.
practical. However, the exciter time constant is much smaller
than generator time constant in rotary excitation control
systems. As the loop gain increases, the poles move toward
the corresponding zeros. Since the two time constants are
well separated, the effect of nonexact pole–zero cancellation
is not detrimental.
The cancellation method provides for an extremely stable
system with very minimum voltage overshoot and the field
loop gains
voltage remains very stable even with high
. Fig. 11 shows the
voltage response of a 100-MW steam turbine generator using
pole–zero cancellation gains.
The closed- and open-loop Bode plots are, respectively, il-
lustrated in Figs. 12 and 13 when the pole–zero cancellation
method is used. The gain remains high and the phase lag is com-
pensated for a wide frequency. Again using the 3-dB point that
represents the bandwidth of the excitation system, the phase lag
is 46.3 —a very fast excitation system. Notice the gain re-
mains very flat before it begins to roll off. The flat response il-
lustrates a very stable system with little to no voltage overshoot.
Fig. 13 shows the phase lag of 91 at crossover frequency of
0 dB.
Fig. 13.
open-loop Bode diagram of pole–zero cancellation.
A. Variation Due to Uncertainty in the Loop Gain
Variation due to uncertainty in the loop gain is considered
from the values of 0.1, 0.3, and 1.0. All
by variations in
the other parameters remain unchanged. Fig. 14 illustrates the
responses of the two methods described, pole placement and
pole–zero cancellation, while changing the loop gain ( ) of
the digital controller. Note that both Fig. 14(a) and (c) display
similar rise time but voltage overshoot only occurs using the
pole-placement method in this example. The pole–zero cancel-
lation method provides a means to quickly and accurately tune
the generator excitation system. Faster voltage response can be
achieved by simply increasing the loop gain.
B. Uncertainty in the Knowledge of the Exciter Time Constant
Uncertainty in the knowledge of the exciter time constant is
considered from the values of 0.2, 0.6, and 1.0 s (see Fig. 15).
All other parameters remain unchanged. The comparison
of Fig. 15(a) and (c) indicates the superiority of the perfor-
mance resulting from pole–zero cancellation design over the
V. E
FFECT OF
P
ARAMETER
V
ARIATIONS
The performance of two methods is conducted using com-
puter simulation in the presence of parameter variations. The
parameters considered include system loop gain and uncertain
exciter time constant.
Since, in general, the calculation of loop gain requires several
excitation system parameters that are generally not available
during commissioning, specifically, the machine time constant,
this lack of information can make the use of the pole-placement
approach more time consuming for setup than cancellation ap-
proach.
京公网安备 11010802033920号
Copyright © 2005-2024 EEWORLD.com.cn, Inc. All rights reserved
评论